Inbreeding in Thoroughbreds....a tension between two coefficients

I woke up this morning to a tweet from Henry Field's Newgate Farm in Australia, outlining the success of Extremely Lucky in the Lightning Stakes (L) overnight. A son of the freak Newgate stallion Extreme Choice, Extremely Lucky is inbred 3x3 to the Champion sire Redoute's Choice.

When it comes to inbreeding, the data is fairly clear. The more inbred a horse is, the less likely it is to race and also race at the highest level.

In a 2018 paper Founder-specific inbreeding depression affects racing performance in Thoroughbred horses Todd and colleagues studied the pedigrees of 135,572 Thoroughbred horses and revealed a strong negative relationship between Wright’s inbreeding coefficient, and five measures of racing performance that encompass a range of factors that contribute to exercise performance. These included two measures that were based on the assumption that more successful individuals earn more prizemoney: cumulative prizemoney earnings and prizemoney earnings per start. They also included two measures of constitutional soundness: total number of race starts and career length as well as accounting for consistency of performance with the measure winning strike rate. Interestingly the paper also suggested that there is still considerable genetic load (negative ancestry) within the population of Thoroughbreds.

Similarly, in studying actual genomic inbreeding (as opposed to what ancestry appears in the Stud Book whcih is what Todd studied), Hill and colleagues in their 2022 paper Inbreeding depression and the probability of racing in the Thoroughbred horse found that inbreeding depression is a genome-wide phenomenon significantly impacting on the viability of a horse to ever race. That is, horses that were more inbred in genomic terms, were less likely to race.

The most common practical measurement of inbreeding is Sewall Wright's "F" Coefficient of Inbreeding. Wright, who was interested in improvement in cattle, was thinking of two consequences that matter to a breeder in relation to inbreeding, one consequence being positive, that of uniformity and prepotency, and one being negative, that of loss of vigor and fertility. Wright thought that it would be useful to be able to calculate the degree of inbreeding of an animal because it would make these effects more predictable. His thinking at the time - and applying it to cattle - was that this was important because these two effects were at odds with each other; breeders could increase predictability and uniformity by inbreeding, presumably to superior ancestors, but not without also having detrimental effects on an animal’s health and fertility.

There are some deficits to Wright's F calculation that necessitate the creation of a "work around" to compensate for in applying it to Thoroughbreds. Firstly, the equation considers duplicated ancestors only if they are common to both sire and dam, so if you have a sire that is inbred and a dam that is not inbred to the same ancestors, the inbreeding coefficient as proposed by Wright will underestimate the level of inbreeding for that individual. Secondly, Wright's F equation considers inbred ancestors only if they are duplicated ancestors. So, if you take a stallion like Danehill, who himself is inbred to Natalma 3x3, he would not have an effect on the calculation of the inbreeding coefficient, unless he himself was duplicated in the pedigree. Again, this will underestimate the true level of inbreeding.

However, Wright's F is not the only coefficient that can be used to measure inbreeding within a population. Ancestral inbreeding coefficients have been proposed by Ballou, (1997) J. Hered., 88, 169 and Kalinowski et al., (2000) Conserv. Biol., 14, 1375 as well as an Ancestral History Coefficient (AHC) proposed by Baumung et al (2015).

Ballou first derived a coefficient intended to estimate ancestral inbreeding as the extent to which individual’s ancestors have been subjected to inbreeding. The basic idea behind his method was that an inbred individual with inbred ancestry themselves should be less susceptible to inbreeding depression than an inbred individual with non-inbred ancestors, because those surviving and reproducing inbred ancestors are less likely to be carriers of deleterious alleles.

So in practical terms what the Ballou coefficient suggesting is, the subject horse should be more inbred to horses who themselves are inbred, because those inbred horses have survived and produced within the breed, despite being inbred horses, so they are more likely to be carriers of positive ancestry, not negative ancestry. The obvious horse to think of in this respect is Danehill, a horse inbred 3x3 to Natalma, as much as you can as he has proven both a good racehorse and phenomenal progenitor, despite being inbred. The same would apply to Redoute’s Choice to whom Extremely Lucky is inbred to.

Ballou's coefficient suggests inbreeding to inbred horses as close as you can, however this is countered by Wrights F Coefficient of Inbreeding which measures any inbreeding and as we have discussed, a higher F coefficient has been shown to be deleterious to racetrack performance. So one coefficient is saying, be more inbred to horses who are inbred and survived/prospered, while the other is saying don't be too inbred too closely as the more inbred you are, the less likely you are to be a good racehorse.

This tension between the two is borne out genetically also. In Hill et al's 2022 paper we mentioned above they noted that inbreeding in the distant pedigree, measured as FROH_short in their paper, is not disadvantageous. This observation is in agreement with Todd's 2018 paper that suggested that an ancestral history coefficient of inbreeding (they used the AHC), has a positive association with racing performance and probably captures the effects of positive selection for favourable exercise-relevant traits over many generations. Equally, Hill et al noted that more recently shared common ancestors, indicated in their paper by FROH_long, have a considerable negative impact on the viability of a horse for racing.

Given at this point we don't have the ability to know the short and long genomic inbreeding of each thoroughbred, we are left with Wright's F and Ballou or the AHC to measure these two effects. Later this year, we (myself and Alan Porter) will launch one of our two "COVID projects" in Molecular Matings. This pedigree program uses a host of variables in a machine learning model that retrains each week on data of elite and non-elite racehoses. It is early days yet in terms of the models reliability and robustness but we are able to compute contributions to the score for each variable that is used in the model in order to explain how the model is operating. These contributions can be positive (they make our pedigree score higher) or negative (they make our pedigree score lower). Interestingly we have similar findings to both Todd and Hill's papers above.

In terms of Positive contribution to the model, Ballou's measure of ancestral inbreeding has a high influence while Baumung's Ancestral History Coefficient (AHC) is next. The AHC we have modified to perform on a specific subset of ancestry which we believe had a profound impact on altering the breed in terms of performance, so there is not a high correlation between the two ancestral coefficients.

Equally, the Coefficient of Inbreeding has the largest negative contribution, that is, the higher the Coefficient of Inbreeding, the lower our pedigree score (for those interested, GI is generational interval, the average age in years between the subject horse and its parents; older parents are a negative). This finding is the same as what Todd et al found in their 2018 paper.

In terms of a machine learning model, the two coefficient variables work antagonistically to arrive at an optimum which invariably is that in oreder to maximise the chances of inheriting positive ancestry in the subject horse, it is best to line up a pedigree where the sire and dam have a lot of inbreeding between generations 4 to 8, and even better if that inbreeding is to superior horses who were inbred themselves.